PIRSA:16090032

Feynman Path Integrals Over Entangled States

Green, A. (2016). Feynman Path Integrals Over Entangled States. Perimeter Institute. https://pirsa.org/16090032

Green, Andrew. Feynman Path Integrals Over Entangled States. Perimeter Institute, Sep. 15, 2016, https://pirsa.org/16090032 

          @misc{ pirsa_PIRSA:16090032,
            doi = {10.48660/16090032},
            url = {https://pirsa.org/16090032},
            author = {Green, Andrew},
            keywords = {Other},
            language = {en},
            title = {Feynman Path Integrals Over Entangled States},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {sep},
            note = {PIRSA:16090032 see, \url{https://pirsa.org}}
          }

Andrew Green University College London

DOI 10.48660/16090032
Collection
Talk Type Scientific Series
Subject

Abstract

Entanglement is fundamental to quantum mechanics. It is central to the EPR paradox and Bell’s inequality. Tensor network states constructed with explicit entanglement structures have provided powerful new insights into many body quantum mechanics. In contrast, the saddle points of conventional Feynman path integrals are not entangled, since they comprise a sequence of classical field configurations. The path integral gives a clear picture of the emergence of classical physics through the constructive interference between such sequences, and a compelling scheme for adding quantum corrections using diagrammatic expansions.  We combine these two powerful and complementary perspectives by constructing Feynman path integrals over sequences of matrix product states, such that the dominant paths support a degree of entanglement. We develop a general formalism for such path integrals and give a couple of simple examples to illustrate their utility [arXiv:1607.01778].